Search Results (57)

The combined application of fibers and lightweight aggregates (LWAs) represents an effective approach to achieving high-strength, lightweight concrete. To enhance the predictability of the mechanical properties of fiber-reinforced lightweight aggregate concrete (LWAC), this study conducts an in-depth investigation into its hydration characteristics. In this study, high-strength LWAC was developed by incorporating low water absorption LWAs, various volume fractions of basalt fiber (BF) (0.1%, 0.2%, and 0.3%), and a ternary cementitious system consisting of 70% cement, 20% fly ash, and 10% silica fume. The hydration-related properties were evaluated through isothermal calorimetry test and high-temperature calcination test. The results indicate that incorporating 0.1–0.3% fibers into the cementitious system delays the early hydration process, with a reduced peak heat release rate and a delayed peak heat release time compared to the control group. However, fitting the cumulative heat release over a 72-h period using the Knudsen equation suggests that BF has a minor impact on the final degree of hydration, with the difference in maximum heat release not exceeding 3%. Additionally, the calculation model for the final degree of hydration in the ternary binding system was also revised based on the maximum heat release at different water-to-binder ratios. The results for chemically bound water content show that compared with the pre-wetted LWA group, under identical net water content conditions, the non-pre-wetted LWA group exhibits a significant reduction at three days, with a decrease of 28.8%; while under identical total water content conditions it shows maximum reduction at ninety days with a decrease of 5%. This indicates that pre-wetted LWAs help maintain an effective water-to-binder ratio and facilitate continuous advancement in long-term hydration reactions. Based on these results, influence coefficients related to LWAs for both final degree of hydration and hydration rate were integrated into calculation models for degrees of hydration. Ultimately, this study verified reliability of strength prediction models based on degrees of hydration. Full article

We present a thermodynamically consistent energetic variational model for active nematics driven by ATP hydrolysis. Extending the classical Toner–Tu framework, we introduce a chemo-mechanical coupling mechanism in which the self-advection and polarization dynamics are modulated by the ATP hydrolysis rate. The model is derived using an energetic variational approach that integrates both chemical free energy and mechanical energy into a unified energy dissipation law. The reaction rate equation explicitly incorporates mechanical feedback, revealing how active transport and alignment interactions influence chemical fluxes and vice versa. This formulation not only preserves consistency with non-equilibrium thermodynamics but also provides a transparent pathway for modeling energy transduction in active systems. We also present numerical simulations demonstrating the positive energy transduction under a specific choice of model parameters. The new modeling framework offers new insights into energy transduction and regulation mechanisms in biologically related active systems. Full article

In recent years, an increasing number of published articles on biocatalysis have reported new enzymes that exhibit biotechnologically interesting catalytic activities. Some authors rush to publish their work in an attempt to ensure “novelty” and often present their results with various types of graphs, such as scatter plots or line-and-symbol plots using nonexistent parameters as ordinates, e.g., “Relative Activity (%)” and the like, vs. abscissae such as pH value, temperature, etc. Nevertheless, in vitro enzyme kinetics remains a valuable tool for understanding, optimizing, and effectively applying these biocatalysts under diverse reaction conditions, taking advantage of all available experimental results. This work aims to emphasize the importance of processing experimental data from enzymatic reactions through appropriate fitting with known kinetic equations and to discourage the use of nonexistent parameters. To support this integrated approach, specific examples are provided for the calculation of significant kinetic and thermodynamic parameters, as well as rate constants. Full article

Achieving high-order accuracy in finite difference/spectral methods for space-time fractional differential equations often relies on very restrictive and usually unrealistic smoothness assumptions in the spatial and/or temporal domains. For spatial discretization, spectral methods using smooth basis functions are commonly employed. However, spatial–fractional derivatives pose challenges, as they often lack guaranteed spatial smoothness, requiring non-smooth basis functions. In the temporal domain, finite difference schemes on uniformly graded meshes are commonly employed; however, achieving accuracy remains challenging for non-smooth solutions. In this paper, an efficient algorithm is adopted to improve the accuracy of finite difference/Pertrov–Galerkin spectral schemes for a time-space fractional reaction–diffusion equation, with a hyper-singular integral fractional Laplacian and non-smooth solutions in both time and space domains. The Pertrov–Galerkin spectral method is adapted using non-smooth generalized basis functions to discretize the spatial variable, and the L1 scheme on a non-uniform graded mesh is used to approximate the Caputo fractional derivative. The unconditional stability and convergence are established. The rate of convergence is $O\left(N^{\mu -\gamma }+K^{-min\{\rho \beta ,2-\beta \}}\right),$ achieved without requiring additional regularity assumptions on the solution. Finally, numerical results are provided to validate our theoretical findings. Full article

During crude oil exploration and extraction, the presence of H₂S not only poses a threat to operational safety but also accelerates equipment corrosion, highlighting the urgent need for efficient and cost-effective processing solutions. This study employs a coupled numerical simulation approach that integrates computational fluid dynamics (CFD) and population balance models (PBM) to systematically investigate the multiphase flow characteristics within SK static mixers. By embedding mass transfer rates and reaction kinetics equations for hydrogen sulfide and sodium hypochlorite into the Euler-Euler multiphase flow model using user-defined functions (UDFs), the effects of equipment structure on the efficiency of the crude oil desulfurization process are examined. The results indicate that the optimized SK static mixer (with 15 elements, an aspect ratio of 1, and a twist angle of 90°) achieves an H₂S removal efficiency of 72.02%, which is 18.84 times greater than that of conventional empty tube reactors. Additionally, the micro-mixing time is reduced to 0.001 s, and the coefficient of variation (CoV) decreases to 0.21, while maintaining acceptable pressure drop levels. Using the CFD-PBM model, the dispersion behavior of droplets within the static mixer is investigated. The results show that the diameter of the inlet pipe significantly affects droplet dispersion; smaller diameters (0.1 and 1 mm) enhance droplet breakup through increased shear force and turbulence effects. The findings of this study provide theoretical support for optimizing crude oil desulfurization processes and are of significant importance for enhancing the economic efficiency and safety of crude oil extraction operations. Full article

A set of singularly perturbed systems comprising Fredholm integro-differential equations associated with reaction–diffusion problems is considered. To approximate solutions to these systems, a second-order scheme for the derivatives and the trapezoidal rule for the integral terms are utilized. The discretization is performed on non-standard grids known as Shishkin-type meshes. The numerical method demonstrates a second-order rate of convergence with respect to small parameters in the equations, and error estimates are derived in the discrete maximum norm. Numerical experiments are conducted to verify the theoretical results. Full article

Many important practical problems connected to energy efficiency in buildings, ecology, metallurgy, the development of wireless communication systems, the optimization of radar technology, quantum computing, pharmacology, and seismology are described by large-scale mathematical models that are typically represented by systems of partial differential equations. Such systems often involve numerous input parameters. It is crucial to understand how susceptible the solutions are to uncontrolled variations or uncertainties within these input parameters. This knowledge helps in identifying critical factors that significantly influence the model’s outcomes and can guide efforts to improve the accuracy and reliability of predictions. Sensitivity analysis (SA) is a method used efficiently to assess the sensitivity of the output results from large-scale mathematical models to uncertainties in their input data. By performing SA, we can better manage risks associated with uncertain inputs and make more informed decisions based on the model’s outputs. In recent years, researchers have developed advanced algorithms based on the analysis of variance (ANOVA) technique for computing numerical sensitivity indicators. These methods have also incorporated computationally efficient Monte Carlo integration techniques. This paper presents a comprehensive theoretical and experimental investigation of Monte Carlo algorithms based on “symmetrized shaking” of Sobol’s quasi-random sequences. The theoretical proof demonstrates that these algorithms exhibit an optimal rate of convergence for functions with continuous and bounded first derivatives and for functions with continuous and bounded second derivatives, respectively, both in terms of probability and mean square error. For the purposes of numerical study, these approaches were successfully applied to a particular problem. A specialized software tool for the global sensitivity analysis of an air pollution mathematical model was developed. Sensitivity analyses were conducted regarding some important air pollutant levels, calculated using a large-scale mathematical model describing the long-distance transport of air pollutants—the Unified Danish Eulerian Model (UNI-DEM). The sensitivity of the model was explored focusing on two distinct categories of key input parameters: chemical reaction rates and input emissions. To validate the theoretical findings and study the applicability of the algorithms across diverse problem classes, extensive numerical experiments were conducted to calculate the main sensitivity indicators—Sobol’ global sensitivity indices. Various numerical integration algorithms were employed to meet this goal—Monte Carlo, quasi-Monte Carlo (QMC), scrambled quasi-Monte Carlo methods based on Sobol’s sequences, and a sensitivity analysis approach implemented in the SIMLAB software for sensitivity analysis. During the study, an essential task arose that is small in value sensitivity measures. It required numerical integration approaches with higher accuracy to ensure reliable predictions based on a specific mathematical model, defining a vital role for small sensitivity measures. Both the analysis and numerical results highlight the advantages of one of the proposed approaches in terms of accuracy and efficiency, particularly for relatively small sensitivity indices. Full article

We address the scientific “time” concept in the context of more general relaxation processes toward the Wärmetod of thermodynamic equilibrium. More specifically, we sketch a construction of a conceptual ladder of chemical reaction steps that can rigorously bridge a description from the microscopic domain of molecular quantum chemistry to the macroscopic materials domain of Gibbsian thermodynamics. This conceptual reformulation follows the pioneering work of Kenichi Fukui (Nobel 1981) in rigorously formulating the intrinsic reaction coordinate (IRC) pathway for controlled description of non-equilibrium passages between reactant and product equilibrium states of an overall material transformation. Elementary chemical reaction steps are thereby identified as the logical building-blocks of an integrated mathematical framework that seamlessly spans the gulf between classical (pre-1925) and quantal (post-1925) scientific conceptions and encompasses both static and dynamic aspects of material change. All modern chemical reaction rate studies build on the apparent infallibility of quantum-chemical solutions of Schrödinger’s wave equation and its Dirac-type relativistic corrections. This infallibility may now be properly accepted as an added“inductive law” of Gibbsian chemical thermodynamics, the only component of 19th-century physics that passed intact through the revolutionary quantum upheavals of 1925. Full article

Referencing ion exchange applied in the extraction of ion-adsorption minerals, a mathematical model based on thermodynamic equilibrium has been researched and established to reveal and represent the chemical reaction between minerals and the leaching solution. Meanwhile, a Python-based numerical solver has been developed and programmed to solve the equations of the established model in order to achieve computational efficiency and obtain an accurate solution. Based on the simulation and computation with the established mathematical model, the effects of leaching solution concentration and mineral grade distribution on the extraction of ion-adsorption minerals can be evaluated, validating the set value of 20 g/L for the initial leaching solution concentration and the extraction rate of above 90% for the cut-off grade. Furthermore, the established mathematical model can be integrated into the simulation system for the overall multi-field extraction of ion-adsorption minerals, illustrating the relationship between extracted metal ion concentration in the aqueous phase over time and providing theoretical support for the engineering project. Full article

This study investigates magnetohydrodynamic (MHD) heat and mass transport in a water-based ternary hybrid nanofluid flowing past an exponentially accelerated vertical porous plate. Two critical scenarios are analyzed: (i) uniform heat flux with variable mass diffusion and (ii) varying heat source with constant species diffusion. The model integrates thermal radiation, heat sink/source, thermal diffusion, and chemical reaction effects to assess flow stability and thermal performance. Governing equations are non-dimensionalized and solved analytically using the Laplace transform method, with results validated against published data and finite difference method outcomes. Ternary hybrid nanofluids exhibit a significantly higher Nusselt number compared to hybrid and conventional nanofluids, demonstrating superior heat transfer capabilities. Magnetic field intensity reduces fluid velocity, while porosity enhances momentum transfer. Thermal radiation amplifies temperature profiles, critical for energy systems. Concentration boundary layer thickness decreases with higher chemical reaction rates, optimizing species diffusion. These findings contribute to the development of advanced thermal management systems, such as solar energy collectors and nuclear reactors, enhance energy-efficient industrial processes, and support biomedical technologies that require precise heat and mass control. This study positions ternary hybrid nanofluids as a transformative solution for optimizing high-performance thermal systems. Full article

Apparent kinetics is often used to describe a variety of reactions in the field of chemical looping and solar thermochemical processes, yet a rigorous analytical methodology for utilizing such kinetics has been lacking. The implementation of a novel approach was exemplified in the ceria thermochemical cycle for producing solar thermochemical hydrogen, specifically in the H₂O-driven oxidation step. The H₂ production rate equation was derived, rearranging apparent kinetics from experimental data in the literature into a more suitable analytical form. The 1D model integrates heat transfer, fluid dynamics, and redox chemistry, providing the description of a directly irradiated solar receiver–reactor. Model robustness is ensured through the oxygen mass balance across the cycle, and the comparison against experimental data shows high agreement. The methodology can be useful for simulating chemical looping cycles using any nonstoichiometric oxide, such as ceria-based oxides and, most importantly, oxidation-limited perovskites, for which optimizing the oxidation step in terms of fluid flow, kinetics, and reaction times is crucial. The proposed analytical model can be applied to arbitrarily complex reactor geometries. The inherently local nature of the model also allows the spatial distributions of the redox material’s conversion and utilization to be obtained, paving the way for optimization strategies of the reactor’s design and operation. Full article

Photothermal reactions, involving both photochemical and thermal reaction steps, are the most abundant sequences in photochemistry. The derivation of their rate laws is standardized, but the integration of these rate laws has not yet been achieved. Indeed, the field still lacks integrated rate laws for the description of these reactions’ behavior and/or identification of their reaction order. This made difficult a comprehensive account of the photokinetics of photothermal reactions, which created a gap in knowledge. This gap is addressed in the present paper by introducing an unprecedented general model equation capable of mapping out the kinetic traces of such reactions when exposed to light or in the dark. The integrated rate law model equation also applies when the reactive medium is exposed to either monochromatic or polychromatic light irradiation. The validity of the model equation was established against simulated data obtained by a fourth-order Runge–Kutta method. It was then used to describe and quantify several situations of photothermal reactions, such as the effects of initial concentration, spectator molecules, and incident radiation intensity, and the impact of the latter on the photonic yield. The model equation facilitated a general elucidation method to determine the intrinsic reaction parameters (quantum yields and absorptivities of the reactive species) for any photothermal mechanism whose number of species is known. This paper contributes to rationalizing photokinetics along the same general guidelines adopted in chemical kinetics. Full article

The present study demonstrated an improvement in both 1-heptene conversion and mono-heptyltoluene selectivity. It simultaneously depicted the isomerization reactions of 1-heptene and toluene alkylation over Y zeolite catalysts having a Si/Al of 3.5 and a surface area of 817 m²/g. The physical properties of the fresh zeolite catalyst were characterized using XRD, FTIR, XRF, TPD, and N₂ adsorption–desorption spectroscopy. The experimental part was carried out in a 100 mL glass flask connected to a reflux condenser at different reaction temperatures ranging from 70 to 90 °C, toluene:1-heptene ratios of 3–8, and catalyst weights of 0.25–0.4 g. The highest conversion of ~96% was obtained at the highest toluene:1-heptene ratio (i.e., 8:1), 0.25 g of zeolite Y, at 180 min of reaction time and under a reaction temperature of 90 °C. However, the selectivity of 2-heptyltoluene reached its highest value of ~25% under these conditions. Likewise, the kinetic modeling developed in this study helped describe the proposed reaction mechanism by linking the experimental results with the predicted results. The kinetic parameters were determined by nonlinear regression analysis using the MATLAB^® package genetic algorithm. The ordinary differential equations were integrated with respect to time using the fourth-order Runge–Kutta method, and the resulting mole fractions were fitted against the experimental data. The mean relative error (MRE) values were calculated from the experimental and predicted results, which showed a reasonable agreement with the average MRE being ~11.7%. The calculated activation energies showed that the reaction rate follows the following order: coking (55.9–362.7 kJ/mol) > alkylation (73.1–332.1 kJ/mol) > isomerization (69.3–120.2 kJ/mol), indicating that isomerization reactions are the fastest compared to other reactions. A residual activity deactivation model was developed to measure the deactivation kinetic parameters, and the deactivation energy value obtained was about 48.2 kJ/mol. Full article

This paper presents the results of investigations on the kinetic modeling of Brilliant Blue FCF (BB) discoloration reactions in aqueous solutions with different ozone concentrations and pH conditions. Kinetic studies involve knowledge of the structure and properties of dye and ozone, as well as of the experimental conditions. In general, scientists admit that the predominant oxidation pathway is direct (by free oxygen atoms) or indirect (by free hydroxyl radicals); this will depend on influencing factors such as the physicochemical properties of the dye, the pH of the aqueous solution, ozone concentration, reaction time, and the contact mode with/without stirring. In this experimental research, two pathways were chosen following C_BB = f(t)—1. a constant dye concentration and different ozone concentrations, in the concentration range of 100–250 mg/L, in three pH media (acidic, neutral, and basic), with and without stirring; 2. a constant concentration of ozone and different dyes in the concentration range of 2.5–10 mg/L, under the conditions of point 1. With the obtained experimental data, the curves C_BB = f(t) were drawn and processed according to the integral method of classical kinetics, based on first- and second-order equations. Unfortunately, this simple procedure did not give any results for the pH values studied. The rate constants were negative, and/or the reaction order depended on the initial conditions. Due to its structure, the BB dye has several chromophore groups, and thus multiple attack centers, resulting in several oxidation by-products, which is why the ¹H-NMR spectrum was recorded for the discoloration of BB with ozone. Since the stoichiometry of the overall oxidation reaction, as well as the relationship between the rate constant and the reaction conditions mentioned above, is not known, a kinetic model based on mass transfer coupled with a chain reaction in the bulk liquid phase was proposed and successfully tested at pH = 7. This research approach also involves the consolidation of the theoretical bases of the ozonation process through the kinetic study carried out, as well as the proposal of a kinetic model. These systematics lead to results that are applicable to other aqueous systems that are impure with dyes, allowing for generalizations and the development of the field, ensuring the sustainability of the research. Full article

Four formulations based on the Kirchhoff transformation and time linearization for the numerical study of one-dimensional reaction–diffusion equations, whose heat capacity, thermal inertia and reaction rate are only functions of the temperature, are presented. The formulations result in linear, two-point boundary-value problems for the temperature, energy or heat potential, and may be solved by either discretizing the second-order spatial derivative or piecewise analytical integration. In both cases, linear systems of algebraic equations are obtained. The formulation for the temperature is extended to two-dimensional, nonlinear reaction–diffusion equations where the resulting linear two-dimensional operator is factorized into a sequence of one-dimensional ones that may be solved by means of any of the four formulations developed for one-dimensional problems. The multidimensional formulation is applied to a two-dimensional, two-equation system of nonlinearly coupled advection–reaction–diffusion equations, and the effects of the velocity and the parameters that characterize the nonlinear heat capacities and thermal conductivity are studied. It is shown that clockwise-rotating velocity fields result in wave stretching for small vortex radii, and wave deceleration and thickening for counter-clockwise-rotating velocity fields. It is also shown that large-core, clockwise-rotating velocity fields may result in large transient periods, followed by time intervals of apparent little activity which, in turn, are followed by the propagation of long-period waves. Full article